CN101783017A - Rapid processing method for extracting X-shaped angular point from gray level image - Google Patents

Abstract

The invention relates to a rapid processing method for extracting X-shaped angular points from gray level images. Each X-shaped angular point is formed by bright segments and dark segments in an alternately arranging way. The invention has the advantages that the operation is simple and convenient, the real-time performance is good, the online rapid detection requirements can be satisfied and the like. The method comprises the following steps that: step one: an image pickup device is adopted, images with X-shaped angular points are acquired, the acquired images are transmitted to a computer and are used as images to be detected; step two: pixels to be detected are determined from the images to be detected, and a screening template is used to rapidly screen the X-shaped angular points from the images to be detected according to the symmetry of the images with the X-shaped angular points to obtain candidate X-shaped angular points; and step three: a confirmation template is used to conduct X-shaped angular point identification, confirmation and positioning to the obtained candidate X-shaped angular points.

Description

Be used for extracting the immediate processing method of x type angle point from gray level image

Technical field

The present invention relates to a kind of immediate processing method that is used for extracting x type angle point from gray level image.

Background technology

The identification location of X type angle point is widely used in fields such as Flame Image Process, camera calibration, vision measurement, motion tracking.General angle point extraction algorithm such as harris algorithm, susan algorithm, css method etc.When needs are online when quick and precisely locating X type angle point, there are following problems in present disclosed universal method:

1. do not identify polytype angle point with making any distinction between simultaneously, need carry out the identification of X type angle point the Corner Detection result;

2. need carry out two dimension to the Corner Detection result sequentially screens to avoid that same angle point image is detected a plurality of angle points;

3. the angle point bearing accuracy generally is a pixel level, accurately locatees the occasion of angle point at needs, needs follow-up localization process;

4. computing complexity is difficult to satisfy the requirement of on-line quick detection.

Summary of the invention

Purpose of the present invention is exactly for addressing the above problem, and provides that a kind of to have a computing easy, and real-time is good, can satisfy the immediate processing method that is used for extracting from gray level image X type angle point of advantages such as on-line quick detection requirement.

For achieving the above object, the present invention adopts following technical scheme:

A kind of immediate processing method that is used for extracting X type angle point from gray level image, its step is:

Step 1 adopts picture pick-up device, gathers the image that comprises X type angle point, will collect image and send into computing machine as detected image;

Step 2 is determined pixel to be detected from detected image, then according to the symmetry of X type angle point image, use the screening template, and detected image is carried out the rapid screening of X type angle point, obtains X type candidate angular;

Step 3 is carried out X type angle point recognition and verification location to the X type candidate angular utilization affirmation template that screening obtains.

In the described step 2, definite process of pixel to be detected is that the pixel that is positioned at the some row, column in detected image border is not done detection; In the residual image pixel, only the partial-pixel that is positioned at even number line is detected; Should be with the adjacent pixel to be detected in the delegation every row; If certain pixel to be detected is positioned at odd column, the to be detected pixel neighbouring with it should be positioned at even column; From first upper left pixel to be detected of detected image, successively all pixels to be detected are carried out the Screening Treatment of X type angle point by the row preface.

In the described step 2, be that center, the length of side are in the square-shaped image window of d1 with current pixel to be detected, the 4n at the close window edge of selection (n=1,2,3 ...) individual detection forms the screening template with pixel, the value of n is determined in advance; Forming the detection of screening template determines according to following feature with pixel: any one detection can both be found unique and its detection pixel about the window center symmetry with pixel, it is right that these two detections are formed a symmetrical pixel with pixel, it is right that all detect with 2n symmetrical pixel of pixel composition, is designated as SC _i(i=1,2 ..., 2n); Arbitrary symmetrical pixel is to finding another symmetrical pixel right, and these two symmetrical pixels are to intersecting vertically at the window center place, and all detect with pixel forms n distribution group of pixels, is designated as DQ _j(j=1,2 ..., n).After determining the screening template, before each pixel to be detected screened, be that image window is set up in the image window center in detected image with this pixel to be detected all, the detection of extracting in the window generates the screening template with pixel, so that carry out Screening Treatment.

The use of described screening template is that the Screening Treatment process is:

A calculates in the screening template to begin along clockwise direction n+q near the detection in the detected image upper left corner with pixel and detects the poor of the brightness maximal value of using pixel and minimum value, wherein q ∈ 1,2 ..., n-1} and definite in advance; If this difference greater than threshold value Y1, changes step b over to; If this difference smaller or equal to setting threshold Y1, thinks that then these detections are positioned at same segment with pixel, detected pixel is not an X type angle point, the Screening Treatment of next pixel to be detected in the beginning detected image;

B carries out symmetry and distributivity test to each distribution group of pixels; If distribution group of pixels DQ _jBy symmetrical pixel to SC _kAnd symmetrical pixel is to SC _lForm, calculate the average brightness AV1 of all pixels in the distribution group of pixels, if SC _kMiddle pixel brightness is all greater than AV1 and SC _lMiddle pixel brightness is all less than AV1, or SC _kMiddle pixel brightness is all less than AV1 and SC _lMiddle pixel brightness then carries out step c operation, otherwise other distribution group of pixels is tested equally all greater than AV1; If all the distribution group of pixels does not all satisfy test condition, current pixel to be detected is not an X type angle point, begins the Screening Treatment of next pixel to be detected in the detected image;

After c removed all X type candidate angular records that are positioned at the image window that generates current screening template, writing down current pixel to be detected was X type candidate angular;

D sets up the screening template to the pixel next to be detected of detected image successively, carries out Screening Treatment, obtains all the X type candidate angular in the detected image.

In the described step 3, the method for building up of the affirmation template of X type angle point is: extract to detect with the pixel generation from detected image and confirm template, the detection of confirming template is positioned at current with pixel confirms that the candidate X type angle point that detects is the center of circle, and (d2＞=d1) is on the circumference of diameter to d2; Confirm that the detection in the template forms an end to end detection pixel section with pixel, detect the pixel section by 4m (m=2,3 ...) individual detection forms with pixel, note is the pixel of position 1 in the pixel section near the pixel in the detected image upper left corner wherein, remember that its brightness is I (1), remember successively that in the direction of the clock other pixel locations are i in the detection pixel section, brightness is I (i) (i=2,3, ..., 4m); When candidate X type angle point is confirmed, at first extract and detect pixel section generation affirmation template with identical method, carry out the affirmation operation of X candidate angular then.

The use of described affirmation template confirms that promptly operating process is as follows:

1) calculate to detect in the pixel section all luminance differences between adjacent image point in twos, note S (i) is the luminance difference of i pixel, S (i)=I (i+1)-I (i), and i=1 wherein, 2 ..., 4m-1; And definition S (4m)=I (1)-I (4m);

2) find S (i) (i=1,2 ..., 4m) maximal value in and minimum value S (a) and S (b); If S (a)＞0 and S (b)＜0 then carry out step 3), otherwise current detected X type candidate angular are not X type angle points, begin the affirmation operation of next X type candidate angular;

3) find the symmetrical pixel of S (a); Be in m the continuous pixel of detection pixel section at center with (a+2m) %4m position, finding luminance difference maximal value S (a '), if S (a ')＞0, then carry out step 4); Otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular;

4) find the symmetrical pixel of S (b); Be in m the continuous pixel of detection pixel section at center with (b+2m) %4m position, find luminance difference minimum value S (b '), if S (b ')＜0, then carry out step 5), otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel;

5) subpixel location and affirmation are carried out in current X type candidate angle; A, a ' position pixel detect b in the pixel section in the detection pixel section on the edge in dark space to clear zone, and b ' position pixel is on the edge of clear zone to dark space.Be located in the detected image, the coordinate that detects pixel section a position pixel is (x ₁, y ₁), the coordinate that detects pixel section a ' position pixel is (x ₂, y ₂), the coordinate that detects pixel section b position pixel is (x ₃, y ₃), the coordinate that detects pixel section b ' position pixel is (x ₄, y ₄).If a, a ' position pixel are arranged in the same delegation of image, work as y ₂-y ₁＞=0 o'clock, note a ₁=1000, y ₂-y ₁＜0 o'clock, a ₁=-1000; If b, the same delegation that b ' position pixel is arranged in image works as y ₄-y ₃＞=0 o'clock, note a ₂=1000, y ₄-y ₃＜0 o'clock, a ₂=-1000 also remember

$a_1=\frac{y_2-y_1}{x_2-x_1}$

$b_1=\frac{y_1{x}_2-y_2{x}_1}{x_2-x_1}$

$a_2=\frac{y_4-y_3}{x_4-x_3}$

$b_2=\frac{y_3{x}_4-y_4{x}_3}{x_4-x_3}$

If a ₂-a ₁Absolute value less than 10 ^-3, then current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel; Otherwise straight line aa ' with the intersecting point coordinate of straight line bb ' is:

$x=\frac{b_1-b_2}{a_2-a_1}$

$y=\frac{a_2{b}_1-a_1{b}_2}{a_2-a_1}$

If (x y) is positioned at the circumference inside that generates current affirmation template, and then writing down current X type candidate angular is X type angle point, its subpixel coordinate be (x, y); Otherwise carry out step 6);

6) next X type candidate angular is confirmed operation, all finished affirmation up to all X type candidate angular.

The present invention is directed to the X type angle point design that is widely used in camera calibration, vision measurement and motion tracking, have the following advantages:,, can simplify Target Recognition Algorithms for feature identification provides more definite information to X type angle point sensitivity; To same X type angle point image, only obtain 1 angle point result, need not to carry out two dimension and sequentially screen; Compare with the Trajkovic scheduling algorithm, the present invention has isotropy, is difficult for detecting pseudo-angle point; Can utilize and detect the subpixel location that the intermediate result of confirming is carried out angle point, higher angle point bearing accuracy is arranged; Concrete condition in the time of can being used in combination is adjusted template size, to obtain higher angle point bearing accuracy and identification locating speed; Utilize the rapid screening template of this patent design, can get rid of the non-X type angle point that occupies most of image pixel by quick simple screening, need not to carry out complete detection and location computing for the pixel to be detected that is not angle point and can finish this pixel in advance detecting processing, only possible candidate X type angle point is confirmed to locate computing, can improve detection speed.Experiment shows that algorithm can be handled the PAL-system dynamic image in real time based on microcomputer, need not can realize online in real time X type Corner Detection by hardware.

Description of drawings

Fig. 1 is an X type angle point, and the centre mark place is an X type corner location;

Fig. 2 is the screening template synoptic diagram of X type angle point;

Fig. 3 is the affirmation template synoptic diagram of X type angle point;

Fig. 4 is detected image;

Fig. 5 is detected treatment of picture result.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing and embodiment.

A kind of immediate processing method that is used for extracting X type angle point from gray level image, its step is:

Step 1 adopts picture pick-up device, gathers the image that comprises X type angle point, will collect image and send into computing machine as detected image (Fig. 4);

Step 2 is determined pixel to be detected from detected image, then according to the symmetry of X type angle point image, use the screening template, and detected image is carried out the rapid screening of X type angle point, obtains X type candidate angular; Determining of pixel to be detected: the pixel that is positioned at detected image border 10 row, 10 row is not done detection; In the residual image pixel, only the partial-pixel that is positioned at even number line is detected; Should be with the adjacent pixel to be detected in the delegation every row; If certain pixel to be detected is positioned at odd column, the to be detected pixel neighbouring with it should be positioned at even column; From first upper left pixel to be detected of detected image, successively all pixels to be detected are carried out the Screening Treatment of X type angle point by the row preface.Get d1=9, n=4, promptly in 9 * 9 image window, (P is current pixel to be detected for screening template image window center for A～H, a～h) form screening template (Fig. 2) with pixel to select 16 detections near the window edge; It is right that detection in the screening template is formed 8 symmetrical pixels with pixel: (A, a), (B, b), (C, c), (D, d), (E, e), (F, f), (G, g), (H, h); These 8 symmetrical pixels are to forming 4 distribution group of pixels: (A, a, E, e), (B, b, F, f), (C, c, G, g), (D, d, H, h).Before each pixel to be detected screened, be that image window is set up in the image window center in detected image with this pixel to be detected all, the detection of extracting in the window generates the screening template with pixel, so that carry out Screening Treatment.The use of screening template is that the Screening Treatment process is:

A gets q=3, and Y1=120 calculates A in the screening template, B, C, D, E, F, the brightness maximal value of G pixel and minimum value poor; If this difference greater than threshold value Y1, changes step b over to, continue the current detection pixel is carried out follow-up screening operation; If this difference is smaller or equal to setting threshold Y1, current pixel to be detected is not an X type angle point, begins the Screening Treatment of next pixel to be detected in the detected image;

B carries out symmetry and distributivity test to each distribution group of pixels; Distribution group of pixels (A, a, E, e) by by symmetrical pixel to (A, a) and symmetrical pixel to (E e) forms, calculating pixel A, a, E, e average brightness AV1, if pixel A, a brightness all greater than AV1 and E, e pixel brightness all less than AV1, or A, a pixel brightness all less than pixel brightness among AV1 and E, the e all greater than AV1, then carry out step c operation, otherwise other distribution group of pixels tested equally; If all the distribution group of pixels does not all satisfy test condition, current pixel to be detected is not an X type angle point, begins the Screening Treatment of next pixel to be detected in the detected image;

After c removed all X type candidate angular records that are positioned at the image window that generates current screening template, writing down current pixel to be detected was X type candidate angular;

D sets up the screening template to the pixel next to be detected of detected image successively, carries out Screening Treatment, obtains all the X type candidate angular in the detected image." 0 " mark in the testing result (Fig. 5) the X type candidate angular that obtains after experimental image is screened.

Step 3 is carried out X type angle point recognition and verification location to the X type candidate angular utilization affirmation template that screening obtains.The method for building up of the affirmation template (Fig. 3) of X type angle point is: get d2=11, m=7 is in the image window of 11 pixels in the length of side, chooses 28 pixels and uses pixel for detecting, and forms an end to end detection pixel section.Be that window center foundation affirmation template is confirmed to handle to this X type candidate angular with the X type candidate angular that obtains in the Screening Treatment process successively.The use of affirmation template confirms that promptly processing procedure is as follows:

1) calculate to detect in the pixel section all luminance differences between adjacent image point in twos, note S (i) is the luminance difference of i pixel, S (i)=I (i+1)-I (i), and i=1 wherein, 2 ..., 27; And definition S (28)=I (1)-I (28);

2) find S (i) (i=1,2 ..., 28) in maximal value and minimum value S (a) and S (b); If S (a)＞0 and S (b)＜0 then carry out step 3), otherwise current detected X type candidate angular are not X type angle points, begin the affirmation operation of next X type candidate angular;

3) find the symmetrical pixel of S (a); Be in 7 continuous pixels of detection pixel section at center with (a+14) %28 position, finding luminance difference maximal value S (a '), if S (a ')＞0, then carry out step 4); Otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular;

4) find the symmetrical pixel of S (b); Be in 7 continuous pixels of detection pixel section at center with (b+14) %28 position, find luminance difference minimum value S (b '), if S (b ')＜0, then carry out step 5), otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel;

5) subpixel location and affirmation are carried out in current X type candidate angle; Detect in the pixel section a, a ' position pixel on the edge in dark space to clear zone, " x " mark in the testing result (Fig. 5) a, a ', detect b in the pixel section, b ' position pixel on the edge of clear zone to dark space, "+" mark in the testing result (Fig. 5) b, b '.Be located in the detected image, the coordinate that detects pixel section a position pixel is (x ₁, y ₁), the coordinate that detects pixel section a ' position pixel is (x ₂, y ₂), the coordinate that detects pixel section b position pixel is (x ₃, y ₃), the coordinate that detects pixel section b ' position pixel is (x ₄, y ₄).If a, a ' position pixel are arranged in the same delegation of image, work as y ₂-y ₁＞=0 o'clock, note a ₁=1000, y ₂-y ₁＜0 o'clock, a ₁=-1000; If b, the same delegation that b ' position pixel is arranged in image works as y ₄-y ₃＞=0 o'clock, note a ₂=1000, y ₄-y ₃＜0 o'clock, a ₂=-1000 also remember

$a_1=\frac{y_2-y_1}{x_2-x_1}$

$b_1=\frac{y_1{x}_2-y_2{x}_1}{x_2-x_1}$

$a_2=\frac{y_4-y_3}{x_4-x_3}$

$b_2=\frac{y_3{x}_4-y_4{x}_3}{x_4-x_3}$

If a ₂-a ₁Absolute value less than 10 ^-3, then current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel; Otherwise straight line aa ' with the intersecting point coordinate of straight line bb ' is:

$x=\frac{b_1-b_2}{a_2-a_1}$

$y=\frac{a_2{b}_1-a_1{b}_2}{a_2-a_1}$

If (x y) is positioned at the circumference inside that generates current affirmation template, and then writing down current X type candidate angular is X type angle point, its subpixel coordinate be (x, y), " * " mark in the testing result (Fig. 5) (x, y); Otherwise carry out step 6);

6) next X type candidate angular is confirmed operation, all finished affirmation up to all X type candidate angular.

Experimental data: experimental image is taken the standard test image acquisition by binocular camera, obtains breadth and be 256 grades of gray level images of 1024 * 768.Under identical running environment, classical Harris method and the method for the invention are handled the identical experiment image.It is about 1/4 of the used time of Harris algorithm that the inventive method is extracted the location X type used time of angle point.Utilize the stereoscopic vision positioning principle, adopt algorithm of the present invention and Harris algorithm that the X type angle point in the experimental image is carried out space orientation respectively, and calculate the Euclidean distance of 2 X type angle points, compare with theoretical, the inventive method has higher measuring accuracy, shows that the inventive method has better X type angle point bearing accuracy.Concrete experimental data such as table 1.

Table 1

	Processing time (s)	Distance error scope (mm)	Apart from mean square deviation (mm)
				??Harris	??2.02～2.3	??0.01～1.51	??0.63
The inventive method	??0.5～0.61	??0.016～0.71	??0.31

Claims (6)

1. one kind is used for it is characterized in that from the immediate processing method of gray level image extraction X type angle point its step is:

Step 1 adopts picture pick-up device, gathers the image that comprises X type angle point, will collect image and send into computing machine as detected image;

Step 2 is determined pixel to be detected from detected image, then according to the symmetry of X type angle point image, use the screening template, and detected image is carried out the rapid screening of X type angle point, obtains X type candidate angular;

Step 3 is carried out X type angle point recognition and verification location to the X type candidate angular utilization affirmation template that screening obtains.

2. the immediate processing method that is used for extracting from gray level image X type angle point as claimed in claim 1 is characterized in that in the described step 2, definite process of pixel to be detected is that the pixel that is positioned at the some row, column in detected image border is not done detection; In the residual image pixel, only the partial-pixel that is positioned at even number line is detected; Should be with the adjacent pixel to be detected in the delegation every row; If certain pixel to be detected is positioned at odd column, the to be detected pixel neighbouring with it should be positioned at even column; From first upper left pixel to be detected of detected image, successively all pixels to be detected are carried out the Screening Treatment of X type angle point by the row preface.

3. the immediate processing method that is used for extracting X type angle point as claimed in claim 1 from gray level image, it is characterized in that, in the described step 2, be that center, the length of side are in the square-shaped image window of d1 with current pixel to be detected, select 4n (n=1,2,3 near the window edge,) individual detection forms the screening template with pixel, the value of n is determined in advance; Forming the detection of screening template determines according to following feature with pixel: any one detection can both be found unique and its detection pixel about the window center symmetry with pixel, it is right that these two detections are formed a symmetrical pixel with pixel, it is right that all detect with 2n symmetrical pixel of pixel composition, is designated as SC _i(i=1,2 ..., 2n); Arbitrary symmetrical pixel is to finding another symmetrical pixel right, and these two symmetrical pixels are to intersecting vertically at the window center place, and all detect with pixel forms n distribution group of pixels, is designated as DQ _j(j=1,2 ..., n); After determining the screening template, before each pixel to be detected screened, be that image window is set up in the image window center in detected image with this pixel to be detected all, the detection of extracting in the window generates the screening template with pixel, so that carry out Screening Treatment.

4. the immediate processing method that is used for extracting from gray level image X type angle point as claimed in claim 1 is characterized in that the use of described screening template is that the Screening Treatment process is:

A calculates in the screening template to begin along clockwise direction n+q near the detection in the detected image upper left corner with pixel and detects the poor of the brightness maximal value of using pixel and minimum value, wherein q ∈ 1,2 ..., n-1} and definite in advance; If this difference greater than threshold value Y1, changes step b over to; If this difference smaller or equal to setting threshold Y1, thinks that then these detections are positioned at same segment with pixel, detected pixel is not an X type angle point, the Screening Treatment of next pixel to be detected in the beginning detected image;

B carries out symmetry and distributivity test to each distribution group of pixels; If distribution group of pixels DQ _jBy symmetrical pixel to SC _kAnd symmetrical pixel is to SC _lForm, calculate the average brightness AV1 of all pixels in the distribution group of pixels, if SC _kMiddle pixel brightness is all greater than AV1 and SC _lMiddle pixel brightness is all less than AV1, or SC _kMiddle pixel brightness is all less than AV1 and SC _lMiddle pixel brightness then carries out step c operation, otherwise other distribution group of pixels is tested equally all greater than AV1; If all the distribution group of pixels does not all satisfy test condition, current pixel to be detected is not an X type angle point, begins the Screening Treatment of next pixel to be detected in the detected image;

After c removed all X type candidate angular records that are positioned at the image window that generates current screening template, writing down current pixel to be detected was X type candidate angular;

D sets up the screening template to the pixel next to be detected of detected image successively, carries out Screening Treatment, obtains all the X type candidate angular in the detected image.

5. the immediate processing method that is used for extracting X type angle point as claimed in claim 1 from gray level image, it is characterized in that, in the described step 3, the method for building up of the affirmation template of X type angle point is: extract to detect with the pixel generation from detected image and confirm template, the detection of confirming template is positioned at current with pixel confirms that the candidate X type angle point that detects is the center of circle, and (d2＞=d1) is on the circumference of diameter to d2; Confirm that the detection in the template forms an end to end detection pixel section with pixel, detect the pixel section by 4m (m=2,3 ...) individual detection forms with pixel, note is the pixel of position 1 in the pixel section near the pixel in the detected image upper left corner wherein, remember that its brightness is I (1), remember successively that in the direction of the clock other pixel locations are i in the detection pixel section, brightness is I (i) (i=2,3, ..., 4m); When candidate X type angle point is confirmed, at first extract and detect pixel section generation affirmation template with identical method, carry out the affirmation operation of X candidate angular then.

6. the immediate processing method that is used for extracting from gray level image X type angle point as claimed in claim 5 is characterized in that the use of described affirmation template confirms that promptly operating process is as follows:

1) calculate to detect in the pixel section all luminance differences between adjacent image point in twos, note S (i) is the luminance difference of i pixel, S (i)=I (i+1)-I (i), and i=1 wherein, 2 ..., 4m-1; And definition S (4m)=I (1)-I (4m);

2) find S (i) (i=1,2 ..., 4m) maximal value in and minimum value S (a) and S (b); If S (a)＞0 and S (b)＜0 then carry out step 3), otherwise current detected X type candidate angular are not X type angle points, begin the affirmation operation of next X type candidate angular;

3) find the symmetrical pixel of S (a); Be in m the continuous pixel of detection pixel section at center with (a+2m) %4m position, finding luminance difference maximal value S (a '), if S (a ')＞0, then carry out step 4); Otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular;

4) find the symmetrical pixel of S (b); Be in m the continuous pixel of detection pixel section at center with (b+2m) %4m position, find luminance difference minimum value S (b '), if S (b ')＜0, then carry out step 5), otherwise current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel;

5) subpixel location and affirmation are carried out in current X type candidate angle; A, a ' position pixel detect b in the pixel section in the detection pixel section on the edge in dark space to clear zone, and b ' position pixel is on the edge of clear zone to dark space; Be located in the detected image, the coordinate that detects pixel section a position pixel is (x ₁, y ₁), the coordinate that detects pixel section a ' position pixel is (x ₂, y ₂), the coordinate that detects pixel section b position pixel is (x ₃, y ₃), the coordinate that detects pixel section b ' position pixel is (x ₄, y ₄); If a, a ' position pixel are arranged in the same delegation of image, work as y ₂-y ₁＞=0 o'clock, note a ₁=1000, y ₂-y ₁＜0 o'clock, a ₁=-1000; If b, the same delegation that b ' position pixel is arranged in image works as y ₄-y ₃＞=0 o'clock, note a ₂=1000, y ₄-y ₃＜0 o'clock, a ₂=-1000 also remember

$a_1=\frac{y_2-y_1}{x_2-x_1}$

$b_1=\frac{y_1{x}_2-y_2{x}_1}{x_2-x_1}$

$a_2=\frac{y_4-y_3}{x_4-x_3}$

$b_2=\frac{y_3{x}_4-y_4{x}_3}{x_4-x_3}$

If a ₂-a ₁Absolute value less than 10 ^-3, then current X type candidate angular is not an X type angle point, begins the affirmation operation of next X type candidate angular pixel; Otherwise straight line aa ' with the intersecting point coordinate of straight line bb ' is:

$x=\frac{b_1-b_2}{a_2{-a}_1}$

$y=\frac{a_2{b}_1-a_1{b}_2}{a_2-a_1}$

If (x y) is positioned at the circumference inside that generates current affirmation template, and then writing down current X type candidate angular is X type angle point, its subpixel coordinate be (x, y); Otherwise carry out step 6);

6) next X type candidate angular is confirmed operation, all finished affirmation up to all X type candidate angular.

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